An example of these apparatuses is disclosed in Japanese Patent Application Publication No. 2005-186813, which will be referred to as patent document 1.
The apparatus disclosed in the patent document 1 sets a target speed of a vehicle assisted thereby according to an inter-vehicle distance of the assisted vehicle with respect to a preceding vehicle. The apparatus also estimates the slope, i.e. the gradient or inclination, of a road surface, on which the assisted vehicle is running, according to the driving conditions of the assisted vehicle. Then, the apparatus performs a drive-assist task that corrects the target speed of the assisted vehicle according to the estimated gradient of the road surface. This keeps a suitable inter-vehicle distance of the assisted vehicle with respect to a preceding vehicle.